∆ Galileo and Time.

We can count the swings of a pendulum while another object moves. But this only prove that things can move, and we can compare their motion 'now'.

The first great thinkers of mankind, most probably the
ancient Greeks, were perhaps unfortunately just that, ‘thinkers’.It was apparently first believed by early
philosophers that everything in and about the universe could be understood by the
use of pure thought alone. Some people can't see how one person sitting alone,
‘meditating’ motionless and silently on a mountaintop can learn anything about
the world around them. Let alone about the deepest recesses of the universe.
But this is because they don’t realise the person is in fact directly in
possession of, and exploring in great detail one of the most amazing things we
have found to exist so far. Namely a human brain.Incredibly useful, insightful, and
productive as such ‘meditation’ can be, it also has its limitations because
meditation doesn't involve empirical measurements and rigorous physical
experimentation.

Luckily, at a certain point, people realised that careful physical
experimentation, measurement and calculations, could be used to check and
advance theories and ideas that had originated from thought alone. By
‘experimentation’ simple, repeatable and measurable, real world tests of what
had been suggested by casual observations and thought alone helped feed back accurate
real world results and corrections into the thought process, greatly advancing
the accuracy and direction of our understanding in what was effectively the
birth of ‘scientific process’.

This first leap into Science is often attributed to the
Italian physicist and mathematician ‘Galileo Galilee’, who began experimenting
with pendulums, projectiles, and ‘water clocks’. Therefore perhaps Galileo is the real father, not just
of the scientific method, but of the serious and empirical notion of time. It
is said that he began his work with time as a result of observing the swinging
of ‘the bronze chandelier in the cathedral of pizza (Wikipedia) one day and
comparing their periodic motion to the regular beat of his own pulse.

Galileo realised that, contrary to what we might expect, the
number of heartbeats a lantern took to complete a swing did not decrease
as the lanterns motion reduced. Instead the number of hearbeats per swing remained
virtually the same until the lantern, or pendulum’s, oscillation was too small
to accurately observe. He had therefore discovered one of the most fundamental,
and easy to replicate, principles that was to govern the science of ‘time’ from
that point on.

Now although
comparing human heart beats to lantern swings might seem very inaccurate science
to us these days, it is a fact of science that almost any discovery or
invention can be refined, almost without limit, as it becomes better
understood.

If for example one monitors the number of heart beats a
small simple lantern takes to complete one swing the results would not be very
accurate or useful, but if you replace the un-aerodynamic lantern with a
heavier and more streamlined purpose built pendulum, and compare a greater
number of complete swings or oscillations to your own heat beat, a simple water
clock or even hour glass, you can see how it is logical that you would get more
and more accurate, repeatable and therefore useful results.

Galileo’s observations and refinement of the construction
and understanding of pendulums had incredible consequences for mankind, because while we are used to being surrounded in the modern world
by hyper accurate technology wherever we look understanding the motion of a
pendulum meant that even in in his day and without so much as (an hourglass) a spring
or cog in sight Galileo simply by suspending a dense weight by a length of
twine he could start experimenting with a reliable example of ‘regular periodic
motion’, i.e ‘change’ or what some might call ‘time’, with remarkable
accuracy.

By making the pendulum bob more aerodynamic, heavier and denser,
suspending it over greater lengths, and setting it swinging in draught free
environments, Galileo could have reduced the effects of random influences, and
so refined his accuracy more and more

And so Galileo conducted his own detailed experiments into
the reliable motion of the pendulum and in doing so he made fundamental leaps
in science. His work eventually leading to the invention of the world’s first
accurate mechanical pendulum based clocks.

Figure 4‑1 Analysing a pendulum in 3
dimensions is not usually necessary, so we simplify it to just a simple count,
1,2,3 ... this can give us the idea that linear, one directional time has a
genuine reality.

By comparing motion of a pendulum to his own fairly regular
pulse, Galileo was probably able to realise that in fact the pendulum (whose
only variables would be it’s easily fixed dimensions and mass etc) should have the more reliable and consistent
pattern of motion compared to a human pulse that can be affected by countless
subtle factors. So really it would make more sense to compare the pulse to the
pendulum.

(The first thing we would do (without thinking) is simplify the motion into just one plane)

At this stage Galileo was also comparing his observations
against a form of water clock. Very ingeniously he would compare other examples
of motion to the flow of water from one container to another. The water was
controlled as he blocked or unblocked its flow with his thumb. So in allowing
water to flow as a pendulum completed a known number of swings, Galileo could
then weigh the collected water and use this value to compare to the
swings completed. XXXtidy.

From here on Galileo and others went on to realise that one
could mathematically, or theoretically, understand how and
why a pendulum moved as it did. And go on to see that in theory a ‘perfect
pendulum’ could exist. And then see how purely by working through some mathematical
equations one could tell how the motion of two different pendulums
would compare, without either of them ever actually being constructed or
tested.

This small step from working with real pendulums, heart
beats, regularly flowing water, to working with the mathematical ideas and
equations of theoretical pendulums etc, represents a tremendous step
in science. This because it led to us being able to ‘design’ objects or
machines and calculate how they would perform with great accuracy, before a
single component had actually been made. But this leap may also have been the
first step in us jumping to the conclusion that a thing called ‘Time’ existed.
Time, as something more than just a mental ‘notion’, or ‘mathematical tool’.

Another way of looking at the regular ‘periodic’ motion of a
pendulum would be to realise that if we could see the patterns of light
streaming out for millions of kilometres from a swinging lantern, and freeze
their motion, the pattern of light produced would show, over a very great
distance, a very regular, and evenly spaced ‘wave’ shape.The same kind of repeating curve you would
expect to see if you set up an oscillating pendulum that was constantly
trickling a thin stream of ink onto a conveyor belt of paper moving below.

Figure 4‑2 A one metre pendulum marks
out 300,000 km long repeating patterns of light, but unless we can prove the
past and the future exist, it may be wrong to say it mark out 'seconds of
time'.

In both these cases, the lantern marking out a trail of
light in its surroundings, and a pendulum showing its motion on a moving piece
of paper, the distance between the ‘peaks’ of the waves marked out would always
be very regular (assuming perfect conditions for the sake of simplicity).

From this observation, ‘that pendulums swing with a regular
period’, we get another addition to the idea that not only does the ethereal
‘Time’ exist, but also that time is something that generally
has a smooth and regular nature to it.

In reality all such light or ink trails would really show us
would be a tangible, physical, regularity in the present moment. If for example
we built a swinging lantern of just the right length (CHECK) we would find that
the curving or wave like pattern of light it gave out would produce peaks that
were always around 300,000 km from peak to peak.

We could say that we had built a lantern pendulum that swung
with a period of one second, and that the patterns of light it produced
repeated every 300,000 km because ‘light travels at 300,000 km per second’ –
but all such a conversation, or description, would directly prove would be the
fact that pendulums can exist and be moving in an interesting and restricted way, and location, move in a regular way. And given that light
travels at a fixed rate, regular patterns of light can be created and would be
streaming out from the ‘experiment’ if it was running.

What such an experiment would not prove is that time, or
‘seconds’, or ‘the future’, or ‘the past’, existed, other than as parts of the useful,
mental, ‘notion’ of time.

The usefulness of the ‘notion’ of time.

None of this discussion on ‘pendulums’, effectively
‘clocks’, is meant to in anyway detract from their very real and practical
usefulness. It is however meant to show that while pendulums, or clocks, give
useful and controlled examples of regular motion and change – unless shown
elsewhere - they do not track, or prove the existence of ‘Time’.

To put this another way, we can ask the question…

‘If ‘time’ did
not exist, and objects could ‘just’ move in accordance with the laws of
physics, would a pendulum still be able to do what it does ?’

At this stage the reader may want to say, ‘no’ a pendulum
could not move without time. But this is only because we blindly say
‘objects need time in which to move’. As we will see this implication actually
says nothing, and can be seen as a meaningless circular statement.

However, to show how ‘clocks’ are still useful or essential
even if it is not time that they are measuring, we can consider some of
Galileo’s early experiments and see how he may have thought they proved the
existence of time. While they can actually be interpreted ‘timelessly’ without
losing any real meaning, usefullness or significance.

This might seem contradictory, but remember, what this book
is trying to say is that the world around us is just as we ‘see’ it. Though
we may make the error of over-interpreting what we see in some places, and so
think that there is more to the world than ‘just’ what we observe.

Whether we make the error
of thinking time is more than just a notion or not, everything we do, or make,
apart from ‘time-machines’, will all work fine just as planned. And using the
‘idea’ of time to organise ourselves, our lives, our machines and so on, will
also work. But, as I hope to show this ‘idea of time’ is a subtle
misunderstanding of the observed fact that there is just matter and motion in
existence, and so ‘time’, the past, and the future, are never actually seen
because they simply do not exist.

Given his construction of real and accurate pendulums and
his understanding of theoretical or mathematically perfect pendulums, Galileo
Galilee also went on to methodically explore and mathematically describe the
motion of falling and rolling projectiles.

Seeing and accurately measuring the motion of a falling body
or flying projectile with a modern day movie camera and accurate stopwatch is
pretty easy. Galileo of course had none of these things. But in a stroke of
genius he realised that by using gently sloped ramps or boards he could slow
down the examples of motion he was trying to examine. Making the movement and
trajectories much easier to observe and measure.

If for example we take a stone and throw it straight up into
the air we can clearly see its particular motion but it is very hard to
understand how it changes speed and height during its entire journey.

But if we make a marble as spherical as we can and then roll
it away from us straight up a ramp inclined at say just 10 degrees, then we can
see that while the marble’s motion mirrors that of one being thrown straight up
in the air and returning to our hand, the rolling marble does so in a much
slower and observable way.

Figure 4‑3. Galileo was essentially
comparing the 3d motion of pendulums (X,Y,Z) to the 3d motion of objects moving
on an inclined plane. Doing this in full X,Y,Z detail for both objects would
work perfectly but produce unnecessarily complicated equations.

Figure 4‑4 For mathematical
simplicity Galileo would have just counted each complete swing of the pendulum,
ignoring its more complicated real direction and speed etc.

Just ‘counting’ a pendulum’s complete swings (or
monitoring the amount of water flowing at a steady rate from a container) effectively
produces the idea or ‘notion’ of a ‘non-physical entity - moving steadily in some
way at a constant rate, in a direction not described by any combination of the
dimensions X,Y or Z’.

None of these steps is a problem in itself. But if we
assign the symbol ‘t’ to the ‘mathematical idea’ of some ethereal ‘count’ that
moves or increments regularly and unstoppably in one direction, in a dimension
that we cannot perceive - we may end up (wrongly) thinking that we have added
to the evidence suggesting, or even proving, that the ‘idea’ of time really relates
to a mysterious and intangible – yet genuinely separate and real ‘thing’.
(While in fact ‘t’ just relates to the simple oscillation of energy in the pendulum).

Ramp and roll.

If we roll a marble not just up the ramp and away
from us, but also give it a horizontal motion, its path mimics the
parabola of an airborne projectile in a sedate and easily observable way. Not
only this, but when using an inclined board we can write useful markings and
grids directly on its surface, making the path covered by a moving object even
easier to see and quantify.

So by observing the slower motion of these controlled
objects and, critically, comparing their position at various points in their
journey to the count of his own pulse or far more accurately to the count of
the swings of a carefully constructed pendulum, or a controlled flow of water, Galileo
was able to make very accurate and useful observations of motion.

At this stage Galileo would have been developing equations (XXXcheck)
to explain and quantify his findings. ‘Equations’ are ‘mathematical tools used
to liken, compare or equate’ different things. And specifically Galileo was equating
one form of simple, steady, or regularly repeating, motion to the more varied
and complex movements of hi projectiles as they travelled against the constant
acceleration of gravity, in straight lines (up and down the board) or parabolic
curves.

In his equations he will have at some point used a symbol to
represent the simple steady reference motion of a pendulum or water flow, and
other symbols to represent the speed, direction and position of whatever
‘projectile’ he was comparing this motion to.

Galileo may or may not have used his own word and symbol for
‘Time’ in his writings and equations (CHECK) just as we use ‘t’ today. The
precise symbols or words used are not the point, but it is probable that here
in its appearance as a symbol in his equations the idea of time being something
more than just an idea or notion really became firmly established. REP?

Many great names followed Galileo building on his brilliant work,
Johannes Kepler observed the motion of the planets in the heavens and worked
out that the line from a planet to its sun always marks out ‘equal areas in
equal times’[1].

Following on from Kepler’s work, Sir Isaac Newton using his
discovery or invention of calculus, was able to show mathematically why Kepler’s
observations made such sense. And then to produce extremely accurate equations
explaining the motion of the planets in space, the workings of the law of
gravity, his three laws of motion and countless other very significant discoveries.

Newton carried out all his work on the backbone of the idea
that time was some universally perfect and constant clockwork mechanism
creating a totally reliable yet completely invisible framework of perfectly
regular and universal ‘time’ that ‘ticked at a constant rate throughout all of God’s
creation’.

And this idea of the existence and reliably ridged nature of
time was completely accepted, and functioned perfectly well enough for our
needs, until Albert Einstein revealed that time could not possibly be the
separate and rigid thing is first seemed. Einstein suggested that to explain our
more subtle observations of the universe - in particular some very slight but still
significant inconsistencies in the orbit of mercury - ‘time’ could not be a rigid and separate part of the universe. Instead, he demonstrated that not
only did it seem to make sense to merge space and time together to create
‘Spacetime’, but also tht this Spacetime should be stretchable and warpable !

How and why this is scientifically logical Einstein
explained in great detail in his works on special and general relativity,
theories that have been tested and shown to be fundamentally correct in a
myriad of different ways, not least of which in the workings of every single
Global Positioning Satellite device we use today.

As I hope to show, while it is evidently clear (e.g. from
the fact that GPS clearly works) that relativity is mathematically correct, it
can also be shown that what relativity explains need not be explained in terms
of time existing and being distorted, but instead, just in terms of matter,
forces, and ‘rates of change’ being distorted as described, but simply ‘in the
present’.

So here in an extremely brief history of the idea, and our
work with, Time we seem to have shown how man’s passive observations of the sun’s
natural path through the sky may have led us to make water clocks; How we may
have then moved on to hour-glasses and pendulums; and how we may have
introduced symbols (such as ‘t’) to represent time when we started to create
highly useful, intricate and accurate ‘equations’.

From there how we began mathematically comparing regular and
complex motion, and how all of this work combined with brilliant minds and
careful astronomical observations led us to understand with great clarity the
perfect motion of the planets in the heavens.

But remembering, that with an open mind, we have to consider
equally both possibilities; that time may exist in its own right - and that
time may exist only as a notion. We have to look at this history in two ways.

Is it the history of our discovery and understanding of a
real thing, or is it the history of our creation and development of a very
useful tool or idea?

If we review this rough history from the starting point of
believing that time is real then the answer is obvious; the
observations, experiments, mathematics and subsequent inventions all make
sense. The discoveries and ideas all progress logically, they describe and use
time with more and more refined and reliable accuracy and ultimately, all our
machines and calculations work, so time exists, case closed.

However, if we review the same history more carefully and
without the default assumption that ‘time’ exists and can be used to explain
what we observe, and instead see if it can be explained from a viewpoint that
only ‘matter and motion’ exist, then things become rather interesting.

First we note that our early ancestors only really observed
constant motion. The sun constantly shines and the earth constantly spins on
its axis.

Figure 4‑5 The Sun constantly shines
and the Earth steadily spins, 'days' and 'nights' don’t begin and end, or
'happen' one after the other.

To someone hovering inspace over the north pole with clear
view of everything the simple constatnt rotation of the Earth would be obvious.
But to anyone stuck at a fixed location on the Earth, the Earth seems flat, and
the sun seems to repeatedly appear and disappear. So it seems
not that one constant thing is happening (the Earth spinning) but that
repeatedly, a new though always similar event, ‘sun rise’, keeps happening over
and over. This would seem to be especially true, or ‘obvious’, to people who
didn’t know that the Earth was a sphere spinning in space[2].

The creation of dripping water clocks was really the
creation of our first constant and smoothly or regularly ‘changing’ machines. Machines
made to do no job other than to show some example of such smooth and regular
change, which we then checked against and compared to other motion around us;
and the first motion we compared our clocks to would be the apparently
repetitive motion of the sun.

So far this doesn’t reveal much but If we look carefully at
the point where time seems to start getting credibility as being something real
and measurable, at the point where Galileo started to mathematically compare
heart beats or pendulum swings to the motion of projectiles we can see how some
small and seemingly irrelevant mathematical factors may have been overlooked in
a way that did not affect the accuracy of his results at all by may have led to
falsely strengthening the idea that time is something other than a notion.

These factors are mathematically considerations that in a
strange way should have appeared in his early equations and then been
removed leaving the final results unchanged, so how can they be important?

Imagine Galileo setting up an experiment to observe and
understand the motion of a projectile through the air or across an inclined
plane. The projectile being studied can have its actual position described in
equations by the symbols X,Y and Z, and its speed and direction given by other
appropriate symbols, while for ‘time’ Galileo just needs a single number or
symbol representing the ‘ticks’ of his pendulum, hours, minutes or seconds all
just being arbitrary units of the same ethereal thing.

And so Galileo joins and equates the real motion of the
projectile with the ethereal time, or ‘t’ in his equations, and this works
perfectly.

But hold on, what is the real source of the numbers we put
into thus symbol ‘t’?

Galileo would get his values for ‘t’ from the very real
physical motion of his pulse or a pendulum, each of which are real three
dimensional things that exist and beat, pulse, oscillate, swing, back and
forth i.e. move.

The motion of a pendulum is both simple and complex, we can
see and use its outward simplicity by just counting ‘entire swings’.

But a pendulum bob’s real motion is more complicated. As the
bob swings back and forth it naturally arcs up at each extreme of the swing,
and could also be swinging side to side. So the bob’s real motion is usually a
‘curved up’ ellipse. Galileo could have overcome this problem by just releasing
the pendulum carefully so as not to put any sideways swing on it.

But even then the actual bob itself is always travelling at a
different speed, and with a different acceleration, at every point in its swing.
It even has a speed of zero at each and of its swing, and throughout its motion
its left to right position constantly changes along with its height at every
point.

So nothing about the pendulum bobs motion is really linear,
its speed, its direction, its rate of change of speed, its height or ‘Z’
location, along with its X and Y positions are all constantly changing in
cyclical but still slightly complicated ways.

In comparing a pendulum to the motion of a projectile
Galileo may have been able to write rather complex equations taking all of
these aspects of the pendulums motion also into account. In this way he would
have ended up with equations that would show you precisely where a pendulum bob
would be relative to say the corner of his workshop, perhaps +5 cm X, 2 cm Y
and + 3cm Z, as a projectile being studied was at say 3 metres away X, 2 metres
away Y and .5 metres high Z.

But describing his findings this way would have been
unnecessary, extremely confusing and very counterproductive because precisely
what real world mechanism we use for ‘t’ doesn’t really matter as long as we
use something that results in a steady rate or reliable ‘tick’.

So while Galileo may have been able to write equations
merging the position of a projectile to precisely where and how fast in the X
and Z directions his pendulum bob was he would have very sensibly for
simplicity just kept adding up complete swings of the pendulum and assumed the
existence of some constantly flowing or accumulating number, and so the same
actual results are for convenience expressed in much simpler terms, and with no
real loss of information, for example as ‘at 3 ½ swings the projectile is 5
metres high (Z) and 10 metres away (X)[3].

Now consider that it is a logical fact that Galileo’s
experiments and equations comparing the ‘ethereal’ time to the X,Y and Z motion
of real objects would work in essentially the same way, if instead of comparing
the complex motion of a flying projectile, or a marble rolling in an arc on an
inclined board, to the simplified motion of a pendulum, he had compared the
projectiles complex motion to the even simpler motion of some other real and
physical reference object.

An object whose motion had been made as simple as practical
so that it was just moving in a straight line, at a constant rate, along a
track evenly marked with the numbers 1, 2, 3, 4, 5 and so on.

In realistic terms, particularly with the technology
available to Galileo, it is not only hard to set up an object to move in a
straight line at a constant speed but if you do so you run into many practical
problems. First you need a lot of carefully made track, then the ‘longer’ you
run any experiment the object gets further and further away, it gets harder to
see accurately where the reference object is, it needs its own source of power,
and lastly at the end of any run you have to chase after the reference object
and bring it back![4]

So a human pulse, a water clock, a pendulum, an hour glass,
or as we have now clocks with rotating hands that never move away from the
clock face or even have numerical readouts generally make far more practical
sense than any ‘linear’ device.

If Galileo had made a simple ‘reference object, moving
steadily along a straight track’, instead of using the more complicated motion
of an oscillating pendulum when first exploring the 3dimensional motion of ‘projectiles’
the mathematics would have been simpler and more transparent.

With a linear ‘clock’ he would have been comparing the X, Y
and Z speed, direction, and distance covered by the projectile, with the speed,
distance and direction of the smoothly moving reference object.

However because of the way the track would be constructed
the reference object would, by design have the following properties...

The reference object would
only be moving in one direction, e.g. ‘X’,

The rate this direction was
changing would be zero.

The object’s speed would
be constant in this direction.

And ‘the rate of change of
speed’ of the object in this direction would be zero.

Also, because the object was only moving in the X direction
it would also be true that ...

The rate the reference
object’s direction was changing in the Y axis, would be zero.

The objects speed in the Y
axis would zero.

And the rate of change of
speed of the object in Y direction would be zero.

And also true that...

The rate the reference object’s
direction was changing in the Z axis would be zero.

The objects speed in the Z
axis would zero.

And the rate of change of
speed of the object in Z direction would be zero.

Most of the above details have a value of ‘zero’, and seem mostly
redundant, because all they are effectively saying is ‘that the reference
object moves at an unchanging rate, in some arbitrary but fixed direction’. This
is because when looking for a good sample of steady motion to compare other
motion to, all that matters isthat the
amount of distance the moving object covers when in use constantly increases, at
an unchanging rate.

This breakdown might seem a bit unnecessary, but it is very
important for us to consciously highlight all the factors that Galileo would
have ignored here, because this is effectively what we do when we just
count entire pendulum swings, (or clock ticks) without thinking about their
real origin. Because it is this tiny detail of ignoring a couple of sets of
seemingly irrelevant, zero value, and unchanging numbers, that leads us ending
up with a bizarre ‘one dimensional, steadily progressing’ entity, which seems
to always be there or to have come out of nowhere, as we shall see.

Mathematically comparing the X,Y and Z motion of the ‘straight
line’ reference object with the X,Y and Z motion of the projectile in full
detail would result in a long equation with lots of zero values for the
reference object’s Y and Z speed, position and rate of change of both, and
unchanging values for the objects actual direction, speed, rate of change of
speed, and rate at which the distance it was covering increased.

Not only would it turn out that all of the six separate
‘zero’ values concerning the Y and Z motion can be ignored but the actual X
direction of motion becomes insignificant, any direction will do. And the
actual speed in the chosen direction is also irrelevant as long as it is
constant! (though as we will see in practical terms the fastest speed, and the
most sensible speed to use as a reference will be the fastest speed possible
according to the laws of nature).

Given all this mathematical dead wood it would make great
sense to factor out all of these (9 or 10) zero value, irrelevant or completely
unchanging factors.

XXX POSS SHOW SOME EQUATIONS and ‘zeros’ here.

More realistically in fact any good, let alone excellent
mathematician would probably write out his or her first equations without ever including
these values in the first place knowing they would and still get perfect
mathematical results![5] So
if the job is simplified and the results are still perfect what, you may ask,
is the problem?

The problem is that all the unnecessary baggage described
above can be mathematically factored out of any equation and safely
ignored – safely apart from the fact that it is by ignoring these seemingly
irrelevant details that we end up thinking ‘time’ really exists.

This can happen because it is in the very process of doing
our calculations with just the few numbers relating to the reference object
that do change time seems to ‘appear’ and appear as if it was always there.

In this way time seems to legitimately get the status of
being something apparently universally very real, and functional, while also
being uniquely invisible, one-directional and mysterious.

And it is here that time appears to be something real, that
we have discovered and clarified in our equations. As opposed
to the truth, which is that by using the idea of a set of steadily incrementing
numbers we have created the notion of time. And then by ignoring the true
origin of the idea, we think we have solidified what was at first just a
‘notion’, giving it the status of apparently relating to some scientifically
discovered, real yet mysterious and intangible, continuous, and fourth
dimensional, phenomena or ‘thing’.

Figure - It seems to me that in all equations, (including what I understand about relativistic mathematics), 't' as 'time said to pass in seconds', could be replaced by reference to the position of a pulse of light moving a long a measured and numbed track as above.The point here is that in using the symbol 't' and saying it refers to 'time', we are suggesting that any mathematics that uses 't' and works, also counts as some evidence towards proving the existence and passing of 'time'.Whereas if the above substitution does work, it show that all that is necessary for for such maths to work is 'matter and motion' happening now.

The sudden and unnoticed jump from studying and comparing some
examples of motion, to assuming we have proved the existence of one or more
real and existing features of a thing called ‘time’ happens because when we use
a ‘reference object’ ideally we are looking for, imagining or physically making[6] an
object such that...

The reference object only
moves in one direction,

The direction the
reference object moves in is irrelevant.

Whatever direction the
reference object moves we will insist on calling it ‘forwards’.

It always moves at a
constant and unchanging rate.

It doesn’t matter what
that rate is.

The distance the reference
object is from its real or imaginary start point always ‘theoretically’ or
‘ideally’, increases constantly and unceasingly.

In the moment that we ‘paper over’ the real and simple fact
that all we are actually doing is comparing the motion of two objects, and
instead simplify the numbers for one of the objects for mathematical ease, we
imply that the number whose true origin we papered over is ‘time’. And
while we end up with the mathematics working perfectly, we absolutely
critically, and wrongly, also leave ourselves with a ‘new’ idea or notion.
A notion that we end up thinking relates
to ‘real time’ existing. i.e.

Time – being; ‘The
idea, or notion, of the existence of some extra, invisible, and all permeating, ‘ethereal’
thing. A thing that is constantly moving (or we are moving through) at a fixed
rate, in a direction that ‘doesn’t matter’. Some 4th Dimensional
thing, that can be said to be containing or driving the 3Dimensional objects
and motion we actually see around us.

And something
that can be equally well thought of as either coming towards us, or heading
away from us or just flowing in its own dimension. Or taking us along with it
as it moves along at a steady rate. Powered by something that is unknown, as it
moves in an unstoppable way, never meeting an end point, at a rate that matches
the speed of light.

Time, passing in
a way that both constantly increments or accumulates some ‘past’ numbers or
‘record’ of its passing, while also pulling into existence ‘the future’ from
whatever is ‘ahead’ of it’ .

With any luck by now you can see that the above description,
which seems to match all that we expect of or imagine the mysterious invisible
fourth dimensional entity of ‘time’ to be, is in fact only a description of
what we need from a real or imagined reference object moving in a straight line
at a constant rate, be it a ball on a specially made ramp, or child’s model train
set up to move at a fixed speed along a straight piece of track, so we can use
it as a simple reference object to compare to some other ongoing motion.[7]

And while it seems that like an explorer panning
for gold we have washed away the worthless stuff and been left with or
discovered something valuable this is not quite the case because what we are
left with when we wash away our unnecessary X,Ys and Zs, the symbol ‘t’ that we
use to represent the swinging pendulum is not something that exists and is
discovered but something we have created for our convenience.

You may also see here, how simply comparing some regular
straight line motion, (be it a ball moving along a fixed path, or a toy train
running steadily along a straight piece of track), to some other more
complicated motion and claiming some sensible results - is a far cry from comparing
the motion of two objects, declaring some sensible results, and also
declaring that you have proved the existence of some other ethereal
thing called Time as well.

‘Time’ not just being a real ball or toy train whose
position we are monitoring, as it simply moves along a track until it reaches
the end of the line. But a mysterious thing that moves unstoppably in a fixed
direction, through an invisible fourth dimension, while controlling and
recording the motion of all objects in the universe as it does so!

And from there you can see that given the usefulness of a
reference object moving at a fixed rate in a straight line, but seeing the
impracticalities of this, it is small step to curve the reference objects
groove or ‘track’ into a continuous circle.

Doing immediately this solves both the problem of running
out of track, and of the reference object constantly getting further and
further away as we let it move.

From there of course it is another small step do away with a
rolling ball, or chuffing train, completely and just have a source of energy,
say a weight hanging from a cord wrapped around a drive shaft, or if your
engineering is up to it, just a wound up coil spring, and release that energy
in an orderly way. Say at a rate governed by a swinging pendulum, and then use
that energy to drive a rotating hand at a steady rate. Then you have a
much more manageable, compact and convenient constantly moving reference
object... something we might misleadingly call a ‘clock’ if we insist that just
calling a motorised hand a clock proves the existence of Time.

But also you can hopefully see that, all of these logical
practical steps to produce a convenient reference object to simplify the way we
compare motion make sense, but each of them only actually proves that we can
make machines that efficiently release some supply of energy in a controlled
manner. And none of these steps either points to, or proves the existence of,
some other constantly flowing, invisible, fourth dimensional entity.

[1] POSS ADD Kepler diag. In
fact this expression of kelpers law is just another way of saying that ‘an
orbiting planet always holds the same amount of energy’ – in other-words, while
a planet has a varying distance from its star (in a sense a ‘height it can fall
from’ – or an amount of potential energy) it also has a varying speed (or
amount of potential energy). Adding these two amounts of energy always must
give the same figure (where could the planet gain or lose energy?). thus an
orbiting planet in its elliptical orbit is very similar to a pendulum – holding
the same total energy but swapping it between potential and kinetic smoothly
and reciprocally.

[2] The idea that something else repeatedly starts and
stops is a misunderstanding similar to thinking that a light-house actually
produces flashes of light instead of just a constant stream of light
from source that happens to be constantly rotating.

[3] There is no real loss of
information here because if we know the details of the pendulum used we could
if we wished work out where such a pendulum would be in and X,Y,Z sense at 3 ½
swings.

[4] Note, it would have been
hard for Galileo with his resources to actually create a simple straight line
reference motion because if he had set up a single long gently sloping track to
roll a reference marble the ball would not have moved smoothly and regularly
but would have accelerated faster and faster along the track, he could instead
of used the motion of a strolling donkey or friend along a straight path, etc
but the practicalities of the idea are not the point here.

[5] Which we can assume Galileo
or his followers probably did without thinking much about them.

[7] It may seem at first that
the speed of the reference object would be irrelevant as long as it was
constant but in fact we can't just pick any speed in reality because we
couldn’t make a device that exceeded the speed of light.